Hall algebras are primitively generated

Start: 09/18/2012 - 12:15pm

End: 09/18/2012 - 1:10pm

Speaker:

Jacob Greenstein (UC Riverside)

Abstract:

Hall algebras were introduced by Hall and Steinitz to study combinatorial properties of finite abelian groups. Many years later, they attracted significant interest when Ringel realized quantum groups in terms of Hall algebras of the category of representations of a finite quiver over a finite field and Green found that these are actually bialgebras in a suitably chosen braided tensor category. More recently, cluster algebras were shown to be closely related to Hall algebras. In this talk I will introduce Hall algebras (including the classic ones of Hall and Steiniz) and discuss the problem of finding their presentations. It can be shown that the coalgebra structure of a Hall algebra provides a way of finding generators even if it is not compatible with the algebra structure. (joint work with A. Berenstein)